# Thread: Lipschitz continuous

1. ## Lipschitz continuous

Assume $f: [0, 2\pi] \rightarrow \mathbb{R}$ is Lipschitz continuous. Prove that exists constans $C>0$ that for every $k=1,2...$ there is:
$\int^{2\pi}_{0} f(x) \sin (kx) dx \leq \frac{C}{k}$.